Think about the members of your family. You probably all have some things in common, but you're definitely not all identical! The same is true of a family of lines. What could a family of lines have in common? What might be different? In this Concept, you'll learn about two types of families of lines and how to write general equations for each type of family.
Family 1: The slope is the same
Write the equation for the red line in the image above.
Write the equation for the brown line in the image above.
Write a general equation for each family of lines shown in the images in this Concept.
Now we find the slope of any line perpendicular to our original line:
Sample explanations for some of the practice exercises below are available by viewing the following video. Note that there is not always a match between the number of the practice exercise in the video and the number of the practice exercise listed in the following exercise set. However, the practice exercise is the same in both. CK-12 Basic Algebra: Equations of Parallel and Perpendicular Lines (9:13)
- What is a family of lines?
- Find the equation of the line parallel to 5x−2y=2 that passes through the point (3, –2).
- Find the equation of the line perpendicular to y=−25x−3 that passes through the point (2, 8).
- Find the equation of the line parallel to 7y+2x−10=0 that passes through the point (2, 2).
- Find the equation of the line perpendicular to y+5=3(x−2) that passes through the point (6, 2).
- Find the equation of the line through (2, –4) perpendicular to y=27x+3.
- Find the equation of the line through (2, 3) parallel to y=32x+5.
In 8 – 11, write the equation of the family of lines satisfying the given condition.
- All lines pass through point (0, 4).
- All lines are perpendicular to 4x+3y−1=0.
- All lines are parallel to y−3=4x+2.
- All lines pass through point (0, –1).
- Write an equation for a line parallel to the equation graphed below.
- Write an equation for a line perpendicular to the equation graphed below and passing through the point (0, –1).
2. Write an equation for a line containing (6, 1) and (7, –3).
3. A plumber charges $75 for a 2.5-hour job and $168.75 for a 5-hour job.
Assuming the situation is linear, write an equation to represent the plumber’s charge and use it to predict the cost of a 1-hour job.
5. Sasha took tickets for the softball game. Student tickets were $3.00 and adult tickets were $3.75. She collected a total of $337.50 and sold 75 student tickets. How many adult tickets were sold?